The present invention relates to quantum communication and a quantum computer that employs light, and more particularly to a quantum circuit that effects measurements of quantum states.
The explosive increase in widespread use of the Internet and the practicability of electronic commerce transactions have increased the social needs for encryption technology, which includes maintenance of confidentiality of communications, prevention of forgery, and user authentication. At present, common key methods such as DES (Data Encryption Standard) codes and public key methods including RAS (Rivest, Shamir, Adleman Public Key Encryption) codes are in wide use. However, these methods are based on xe2x80x9csafety through computational load,xe2x80x9d and current encryption methods are therefore always threatened by progress in computer hardware and code decryption algorithms.
The laws of physics, in contrast, guarantee the safety of xe2x80x9cphysical codesxe2x80x9d such as quantum codes, and these physical codes therefore can guarantee ultimate safety that does not depend on limitations of the capabilities of computers. Putting such an encryption method into practical use would have an extremely powerful social impact, and such encryption methods are expected to become one of the technological foundations of the information industry in the future.
The transmission of quantum information, of which quantum code is representative, is limited to a distance of several tens of kilometers due to loss and disturbance of the quanta (photons) that are used in transmission. In addition, intercommunication is limited to the two ends of the optical fiber that makes the transmission path, and quantum communication with multiple partners therefore requires the establishment of a large number of optical fibers. To solve these problems and realize quantum networking that can implement quantum information communication over a wide range requires technology such as relays and exchanges. Of course, relays and exchanges can be realized by converting quantum information to classical information at a relay station, but such a solution would interrupt the advantageous properties inherent in quantum information communication. In a case in which quantum encryption keys are distributed, for example, a wire-tapper could obtain access to all information by breaking into a relay station, and the safety against wiretapping that is the advantage of quantum information would be lost.
For these reasons, there is a need for quantum relays and quantum exchanges that relay and exchange quantum information as is. Quantum relays and quantum exchanges are also vital for distributed quantum computers. The utilization of quantum teleportation by a quantum relay can realize various effects as described hereinbelow. Quantum information is carried by entangled photon pairs that imply quantum correlation and by classical information separately. When entanglement swapping is used, transmission can be implemented by swapping entangled photon pairs at successive repeaters. The sender provides the swap information to the receiver as classical information.
By means of this entanglement swapping method, the receiver and sender can share entangled photon pairs even when separated by great distances.
Quantum teleportation and entanglement swapping are predicated on the generation of entangled photon pairs and the measurement of Bell states. In Bell-state measurement, two photons are discriminated to be in one of four entangled states, referred to as Bell states. Although the principles of quantum teleportation and entanglement swapping have been confirmed through experimentation, it is not possible with the currently available technology to discriminate all of four Bell states, and transmission by any desired quantum state is therefore yet to be realized.
In Science, 282, 706 (1998), Furusawa, A. et al. reported on quantum teleportation that does not require measurement of Bell states. Although this method enables transmission in any quantum state, it entails 100% squeezing of light. However, due to the insufficient squeezing of the light source that is currently obtainable, the obtainable fidelity of the transmitted quantum states is no higher than 58%. Nevertheless, a fidelity of nearly 100% can be expected if Bell-state measurement can be realized.
For the measurement of Bell states, methods are normally adopted that employ detection circuits composed of photon detectors and linear-optical elements such as semitransparent mirrors and polarization beam splitters. However, such methods can discriminate only two of the four Bell states.
The Bell state of two photons can be represented in the framework of concept of the linear-optics by the following equations:
"PHgr"(xc2x1)=(|x greater than |x greater than xc2x1|y greater than |y greater than )/2xc2xdxe2x80x83xe2x80x83(1)
xcexa8(xc2x1)=(|x greater than |y greater than xc2x1|y greater than |x greater than )/2xc2xdxe2x80x83xe2x80x83(2)
where |x greater than  and |y greater than  are the state functions for photons polarized in the directions of the x-axis and the y-axis, respectively.
As can be understood from equations (1) and (2), a Bell state is a superposed state of a two-photon state specified by a set of two directions of polarization and the state specified by the exchanged directions of polarization of two photons. "PHgr"(xc2x1) are states in which the two photons polarize in the same direction, the state being symmetrical (+) or antisymmetrical (xe2x88x92) with respect to exchange of the directions of polarization; and xcexa8(xc2x1) are states in which the two photons polarize in orthogonal directions, the state being symmetrical (+) or antisymmetrical (xe2x88x92) with respect to the exchange of the direction of polarization.
FIG. 1 shows the configuration of an example of a Bell-state measurement circuit of the prior art that employs linear-optical elements.
The Bell-state measurement circuit is constituted by linear-optical elements including semitransparent mirror 51 and polarization beam splitters 52 and 53, and photon detectors 54, 55, 56, and 57. Polarization beam splitters 52 and 53 split incident polarized light into s-polarized light that oscillates in a direction perpendicular to the plane of incidence, and p-polarized light that oscillates within the plane of incidence. Photon detectors 54 and 55 detect s-polarized light and p-polarized light, respectively, emerging from polarization beam splitter 52. Photon detectors 56 and 57 detect the s-polarized light and p-polarized light, respectively, emerging from polarization beam splitter 53.
Polarized light of one of the four Bell states is incident on this Bell-state measurement circuit. The possible Bell states obtained from the response of photon detectors 54-57 are shown in Table 1.
As can be seen from Table 1, the Bell-state measurement circuit realized by the linear-optical elements shown in FIG. 1 can discriminate the xcexa8(xc2x1) states but cannot discriminate one of the "PHgr"(xc2x1) states. Although it is known that the use of a quantum gate, referred to as a light-controlled NOT gate, enables all four Bell states to be discriminated, a practically realizable device of this type of quantum gate has still not been known.
Scully M. O. et al. have recently proposed in Physical Review Letters 83, 4433 (1999) a method of measuring Bell states that employs two-photon absorption. In this method, the Bell states are specified in terms of circularly polarized light, the light is passed through three atomic cells to cause two-photon absorption, and the fluorescence emitted from the atomic cell caused by two-photon absorption is observed. The absorption of only one specific Bell state can be caused if the atoms in the cells are prepared in advance by a strong electromagnetic field such that the atomic wave function is represented in a special superposition of unperturbed atomic wave functions. The Bell state of the incident light can thus be determined by observing which cells absorb light. If two-photon absorption does not occur in any of the three cells, it can be concluded that the incident light was in the remaining one Bell state.
The two-photon absorption in the method of Scully et al. uses atoms that have been prepared in advance by a strong electromagnetic field such that their wave function has a specific superposed state. However, it is difficult to keep the state of the atoms in the prepared state in which a plurality of states are superposed. Moreover, the method of Scully et al. necessitates three cells containing the atoms that have been thus prepared. Furthermore, since the atoms are contained in the cells as a gas, the atoms have a low density and the probability of two-photon absorption is low. To obtain two-photon absorption with sufficiently high probability, the cells must be extremely long, and this renders the method impractical. Still further, since the probability of observing fluorescence from electrons that have been excited by two-photon absorption is also not high, there is a high probability of error in discriminating the Bell states when fluorescence can not be observed. Transmission of quantum states cannot be achieved with high fidelity if errors occur in discriminating the Bell states.
It is a principal object of the present invention to provide a practical quantum circuit capable of measuring Bell states using a material that absorbs photon pairs with sufficiently high probability and that does not require setup of atomic states by means of an external electromagnetic field in order to realize communication of quantum states with high fidelity.
The quantum circuit of the present invention is provided with: a two-photon absorbing crystal having the crystal symmetry selected so that the two-photon absorbing crystal selectively absorbs a photon pair of a prescribed Bell state in accordance with selection rules based on crystal symmetry; and a two-photon absorption detector that detects absorption of photon pairs by said two-photon absorbing crystal.
The quantum state of an incident optical signal is a state in which four Bell states are superposed or entangled and it is intended that one of the entangled four Bell states is discriminated by means of the two-photon absorption by the crystal having a crystal symmetry that permits two-photon absorption of a polarized photon pair in the Bell state to be discriminated.
If the two-photon absorbing crystal has crystal symmetry that permits two-photon absorption of a polarized photon pair in any one of a plurality of Bell states that correspond to degenerated final states of exciton production in said two-photon absorbing crystal, a perturbation field is applied to said crystal so that the two-photon absorbing crystal will selectively absorb the polarized photon pair in only one of the plurality of the Bell states.
Electrons that are excited by two-photon absorption are detected by the two-photon absorption detector. The use of polarization elements enables the one-to-one conversion of one Bell state to another Bell state. All of the Bell states can be discriminated by successively repeating the operations of: converting the Bell state of a photon pair that have been transmitted by a two-photon absorbing crystal, to another Bell state; directing this photon pair to another two-photon absorbing crystal; and detecting.
The quantum states of polarized light include the four Bell states "PHgr"(+), "PHgr"(xe2x88x92), xcexa8(+), and xcexa8(xe2x88x92).
"PHgr"(+) is a state in which the directions of polarization of the photon pair are the same and that is symmetrical with respect to the exchange of the directions of polarization; "PHgr"(xe2x88x92) is a state in which the directions of polarization of the photon pair are the same and that is antisymmetrical with respect to t he exchange of the directions of polarization; xcexa8(+) is a state in which the directions of polarization of the photon pair are orthogonal and that is symmetrical with respect to the exchange of the directions of polarization; and xcexa8(xe2x88x92) is a state in which the directions of polarization of the photon pair are orthogonal and that is antisymmetrical with respect to the exchange of the directions of polarization.
The above-described quantum circuit requires four two-photon absorbing crystals to discriminate the four Bell states "PHgr"(+), "PHgr"(xe2x88x92) xcexa8(+) and xcexa8(xe2x88x92). However, since two states xcexa8(+) and xcexa8(xe2x88x92) can be discriminated by using a prior-art quantum circuit as shown in FIG. 1 using linear-optical elements, it suffices for the "PHgr"(+) state and "PHgr"(xe2x88x92) state ( which cannot be discriminated by linear-optical elements), to be absorbed by two-photon absorbing crystals and detected, and for the remaining xcexa8(+) and xcexa8(xe2x88x92) states to be discriminated by linear-optical elements.
The quantum circuit to discriminate two Bell states such as "PHgr"(+) and "PHgr"(xe2x88x92) states is constituted by: a first two-photon absorbing crystal having the crystal symmetry selected so that the two-photon absorbing crystal selectively absorbs a photon pair of a first prescribed Bell state in accordance with selection rules based on crystal symmetry; a first two-photon absorption detector that detects absorption of photon pairs by the two-photon absorbing crystal; a second two-photon absorbing crystal having the crystal symmetry selected so that the two-photon absorbing crystal selectively absorbs a photon pair of a second prescribed Bell state in accordance with selection rules based on crystal symmetry; a second two-photon absorption detector for detecting the absorption of photon pairs by said second two-photon absorbing crystal; and a first polarization element that converts a first transmitted Bell state to the second prescribed Bell state.
Here the first transmitted Bell state is one of the possible Bell states of a polarized photon pair that have been transmitted by said first two-photon absorbing crystal.
As an embodiment of this quantum circuit, if the first and second two-photon absorbing crystals are both crystals that absorb the "PHgr"(+) Bell state, the above-described first and second prescribed Bell states are both "PHgr"(+). Then, if the first transmitted Bell state is "PHgr"(xe2x88x92), a polarization element that converts Bell state "PHgr"(xe2x88x92) to Bell state "PHgr"(+) is used as the first polarization element. In this case, the first polarization element can be a retarder means that provides a 90xc2x0 phase difference between the oscillations in polarization directions of each photon of the photon pair.
In this way, the discrimination of Bell states "PHgr"(+) and "PHgr"(xe2x88x92) from the incident polarized light is enabled.
As the polarization element, a retarder can be used that provides a 90xc2x0 phase difference between the oscillations in polarization directions of each photon of the photon pair when converting from Bell state "PHgr"(xc2x1) to Bell state "PHgr"(∓) Conversion from Bell state "PHgr"(xc2x1) to Bell state xcexa8(∓) can also be realized by arranging an optical rotator of 90xc2x0 rotation in one of the photon paths. The conversion from xcexa8(xc2x1) to xcexa8(∓) is achieved by retarders for providing a 90xc2x0 phase difference between the oscillations in polarization directions of one of the photon pair and a xe2x88x9290xc2x0 phase difference to the oscillations of the other photon.
Generally, the absorption of photons of Bell state "PHgr"(xe2x88x92) is weaker than the absorption of photons of Bell state "PHgr"(+), and the absorption of photons of Bell state xcexa8(xe2x88x92) is weaker than the absorption of photons of Bell state xcexa8(+). As a result, a crystal having a crystal symmetry that absorbs photons having Bell state "PHgr"(+) or photons having Bell state xcexa8(+) is used as the two-photon absorbing crystal.
Accordingly, polarization elements are also used that convert to Bell state "PHgr"(+) or to Bell state xcexa8(+).
According to the present invention, each of the four Bell states is discriminated by a different discrimination means, and as a result, even in the event of discrimination failures, the possibility of discriminating an incorrect Bell state is limited to failures caused by noise of the detectors and is therefore small. Bell-state discrimination can therefore be realized with a low level of error.
The discrimination of all Bell states in the present invention is thus realized by the discrimination of specific Bell states by quantum interference and polarization selection rules of two-photon absorption that are based on the symmetry of a crystal and by the conversion of Bell states by polarization elements; and there is consequently no need for preparations in advance such that the wave functions of an atom are employed with particular superposition.
In addition, strong two-photon absorption can be expected because a solid is used. As a result, a practical quantum circuit can be realized that can absorb photon pairs with sufficiently high probability and discriminate Bell states using a material that does not require the preparation of the state of an atom by an external electromagnetic field.
Although extremely rapid phase relaxation is normally a problem in quantum circuits that employ a solid material, the effect of phase relaxation is not a problem in the present invention because electrons that have been excited by two-photon absorption need not maintain coherence.
The above and other objects, features, and advantages of the present invention will become apparent from the following description referring to the accompanying drawings which illustrate examples of preferred embodiments of the present invention.